Model Validation and Selection in Metabolic Flux Analysis and Flux Balance Analysis

13C-Metabolic Flux Analysis (13C-MFA) and Flux Balance Analysis (FBA) are widely used to investigate the operation of biochemical networks in both biological and biotechnological research. Both of these methods use metabolic reaction network models of metabolism operating at steady state, so that reaction rates (fluxes) and the levels of metabolic intermediates are constrained to be invariant. They provide estimated (MFA) or predicted (FBA) values of the fluxes through the network in vivo, which cannot be measured directly. A number of approaches have been taken to test the reliability of estimates and predictions from constraint-based methods and to decide on and/or discriminate between alternative model architectures. Despite advances in other areas of the statistical evaluation of metabolic models, validation and model selection methods have been underappreciated and underexplored. We review the history and state-of-the-art in constraint-based metabolic model validation and model selection. Applications and limitations of the χ²-test of goodness-of-fit, the most widely used quantitative validation and selection approach in 13C-MFA, are discussed, and complementary and alternative forms of validation and selection are proposed. A combined model validation and selection framework for 13C-MFA incorporating metabolite pool size information that leverages new developments in the field is presented and advocated for. Finally, we discuss how the adoption of robust validation and selection procedures can enhance confidence in constraint-based modeling as a whole and ultimately facilitate more widespread use of FBA in biotechnology in particular.